# 269edo

 ← 268edo 269edo 270edo →
Prime factorization 269 (prime)
Step size 4.46097¢
Fifth 157\269 (700.372¢)
Semitones (A1:m2) 23:22 (102.6¢ : 98.14¢)
Dual sharp fifth 158\269 (704.833¢)
Dual flat fifth 157\269 (700.372¢)
Dual major 2nd 46\269 (205.204¢)
Consistency limit 3
Distinct consistency limit 3

269 equal divisions of the octave (abbreviated 269edo or 269ed2), also called 269-tone equal temperament (269tet) or 269 equal temperament (269et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 269 equal parts of about 4.46 ¢ each. Each step represents a frequency ratio of 21/269, or the 269th root of 2.

269edo is inconsistent in the 5-odd-limit and the errors of both harmonics 3 and 5 are quite large. The patent val tempers out 6144/6125 in the 7-limit, 540/539 and 5632/5625 in the 11-limit and 364/363 and 676/675 in the 13-limit. The 269c val tempers out 225/224 and 4375/4374 in the 7-limit, and 269ce 385/384 in the 11-limit, so that it supports and provides an excellent tuning for catakleismic and marvel temperaments.

### Odd harmonics

Approximation of odd harmonics in 269edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -1.58 +1.79 -0.80 +1.29 +1.84 -1.87 +0.21 +2.11 +1.37 +2.08 +0.72
Relative (%) -35.5 +40.1 -17.8 +29.0 +41.3 -41.8 +4.6 +47.2 +30.7 +46.7 +16.2
Steps
(reduced)
426
(157)
625
(87)
755
(217)
853
(46)
931
(124)
995
(188)
1051
(244)
1100
(24)
1143
(67)
1182
(106)
1217
(141)

### Subsets and supersets

269edo is the 57th prime edo.